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4vir4ik [10]
2 years ago
6

O is the centre of the circle and ABC and EDC are tangents to the circle. Find the size of angle BCD. You must give reasons in y

our answers.

Mathematics
1 answer:
Simora [160]2 years ago
7 0

Answer:

mBCD = 28°

Step-by-step explanation:

The angle mBFD inscribes the arc mBD, so we have that:

mBFD = mBD/2

76 = mBD/2

mBD = 152°

The angle mBOD is a central angle related to the arc mBD, so we have that:

mBOD = mBD = 152°

In the quadrilateral BODC, the sum of internal angles needs to be equal to 360° (property of all convex quadrilaterals). The angles mCBO and mCDO are right angles, because EDC and ABC are tangents to the circle.

So, we have that:

mBOD + mCDO + mBCD + mCBO = 360

152 + 90 + mBCD + 90 = 360

mBCD = 360 - 90 - 90 - 152

mBCD = 28°

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JulsSmile [24]

(1) x represents the number of apples bought, y represents the number of bananas.

(2) each term represents the total costs of a given fruit, so 0.50x is the total cost of apples and 0.30y is total cost of bananas.

(3) The coefficients are unit prices: coefficient 0.50 is the price of 1 apple, 0.30 is the price of 1 banana.

3 0
2 years ago
A plane intersects the center of a sphere with a volume of about 113.1 m3. What is the area of the cross section? Round to the n
ivolga24 [154]

Answer:

Step-by-step explanation:

if ~radius=r \\volume =\frac{4}{3} \pi r^3\\113.1=\frac{4}{3} \pi r^3\\113.1 \times \frac{3}{4 \pi } =r^3\\\frac{339.3 }{4 \times 3.14} =r^3\\r^3=\frac{339.3}{12.56} \approx 27\\r=3\\area =\pi r^2=\pi *3^2=9\pi =9*3.14=28.26 \approx 28.3 ~m^2

5 0
2 years ago
The dye dilution method is used to measure cardiac output with 3 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)
Lemur [1.5K]

Answer:

Cardiac output:F=0.055 L\s

Step-by-step explanation:

Given : The dye dilution method is used to measure cardiac output with 3 mg of dye.

To Find : Find the cardiac output.

Solution:

Formula of cardiac output:F=\frac{A}{\int\limits^T_0 {c(t)} \, dt} ---1

A = 3 mg

\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt

Do, integration by parts

[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0

[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0

[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}

[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}

[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}

[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}

Substitute the value in 1

Cardiac output:F=\frac{3}{54.49}

Cardiac output:F=0.055 L\s

Hence Cardiac output:F=0.055 L\s

4 0
2 years ago
How can the triangles be proven similar by the SSS similarity theorem? Show that the ratios StartFraction U V Over X Y EndFracti
dangina [55]

Answer:

<u>option 1</u>

Step-by-step explanation:

The question is as shown in the attached figure.

From the figure, we can deduce that:

∠U ≅ ∠X and ∠W ≅ ∠Z  and ∠V ≅ ∠Y

So, ΔUWV similar to ΔXZY

But it is required to know " How can the triangles be proven similar by the SSS similarity theorem? "

So, we need to prove the corresponding angles are proportion

With the help of the previous corresponding angles.

So, we need to show that the ratios \frac{UV}{XY}  \ , \ \frac{WU}{ZX} \  and \ \frac{WV}{ZY} are equivalent.

So, the answer is <u>option 1</u>

5 0
2 years ago
A shipping company borrows $70 million at 5% p.a. compound interest to build a new cruise ship. If it repays the debt after 3 ye
dem82 [27]

Answer:

about 11.03 million

Step-by-step explanation:

Use the equation I = P(1+r/100)^n - P (I is the compound interest, P is the principle, r is the rate percent, and n is the number of years):

Substitute the values given:

I = 70,000,000(1 + 5/100)^3 - 70,000,000

Use a calculator to solve and you will get ~11.03 million.

5 0
2 years ago
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